Solve the initial value problem: --(; "). ) - (:). æ' 81 ӕ, æ(0) = x1(t) x2(t)

An economist is interested in how the price of a certain item affects its sales. When the price of the item is $ p, the number of items sold will be q = f(p). (This is the idea of "demand") Suppose we found out that f(150) = 2,000 and that f'(150) = -25. (a) Sketch the information of two boldface statements in a quick picture/sketch: (b) Write out in words what the first statement f(150) = 2,000 means in the context. (c) The fact that the derivative is negative reflects what natural phenomenon? (d) Write out in words what the statement f'(150) = -25 means in the context. (Add in appropriate units!) (e) Use the information given to estimate f(151) and f(149.5). Show your work, and explain your rationale for proceeding as you did. A little picture would be ideal to explain your thinking.

Is there any value of x that satisfies the equation below? In(x) = -e"

Suppose that ?(?) is a function with ?(95)=76 and ?′(95)=6. Estimate ?(97.5).